Question: $\dfrac{d}{dx}\left(\dfrac{1}{x^9}\right)=$
Explanation: The strategy We can first rewrite the fraction as a negative power of $x$. Then, the derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is negative.) Rewriting the fraction as a negative power $\dfrac{1}{x^9}=x^{-9}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{-9}\right) \\\\ &=-9x^{-9-1} \gray{\text{The power rule}} \\\\ &=-9x^{-10} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(\dfrac{1}{x^9}\right)=-9x^{-10}$. This can also be written as $-\dfrac{9}{x^{10}}$ (all equivalent forms are accepted).